Topology-Based Approach to Predict Relative Stabilities of Charged and Functionalized Fullerenes

Understanding the relationship between structure and stability is one of the fundamental aspects of fullerene chemistry, as the number of possible cage isomers is very large and complexity increases by orders of magnitude when chemical groups are attached to the fullerene cage. The well-established stability rules valid for neutral fullerenes do not apply to many charged or functionalized fullerenes. Here we present the theory, implementation, and applications of two simple topology-based models that allow one to predict the relative stability of charged and functionalized fullerenes without the need for quantum chemistry calculations: (i) the charge stabilization index (CSI) model, based on the concepts of cage connectivity and frontier π orbitals, which offers a general framework for the relative stability of both positively and negatively charged fullerenes, as well as endohedral metallofullerenes, and (ii) the exohedral fullerene stabilization index (XSI) model, which incorporates all key factors governing the stability of exohedral fullerenes, namely, π delocalization, σ strain, and steric hindrance between addends. Based exclusively on topological information, both models are powerful prescreening tools for predicting the most stable structures of a large number of charged and functionalized fullerenes. For easy use by fullerene chemists, both models have been implemented in the FullFun (for Fullerene Functionalization) software package, whose effectiveness and efficiency are demonstrated by some illustrative examples.